Properties

Label 2.2.281.1-14.2-d
Base field \(\Q(\sqrt{281}) \)
Weight $[2, 2]$
Level norm $14$
Level $[14, 14, -w + 8]$
Dimension $23$
CM no
Base change no

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Base field \(\Q(\sqrt{281}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 70\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[14, 14, -w + 8]$
Dimension: $23$
CM: no
Base change: no
Newspace dimension: $79$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{23} + x^{22} - 36x^{21} - 35x^{20} + 555x^{19} + 518x^{18} - 4806x^{17} - 4247x^{16} + 25782x^{15} + 21262x^{14} - 89175x^{13} - 67703x^{12} + 200759x^{11} + 138917x^{10} - 290201x^{9} - 182400x^{8} + 258952x^{7} + 148223x^{6} - 131540x^{5} - 68684x^{4} + 32008x^{3} + 14940x^{2} - 2335x - 820\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 8]$ $-1$
2 $[2, 2, -w + 9]$ $\phantom{-}e$
5 $[5, 5, -76w + 675]$ $...$
5 $[5, 5, 76w + 599]$ $...$
7 $[7, 7, -8w - 63]$ $...$
7 $[7, 7, -8w + 71]$ $-1$
9 $[9, 3, 3]$ $...$
17 $[17, 17, 42w + 331]$ $...$
17 $[17, 17, 42w - 373]$ $...$
29 $[29, 29, -6w - 47]$ $...$
29 $[29, 29, 6w - 53]$ $...$
31 $[31, 31, 10w + 79]$ $...$
31 $[31, 31, -10w + 89]$ $...$
43 $[43, 43, 2w - 19]$ $...$
43 $[43, 43, -2w - 17]$ $...$
53 $[53, 53, 194w + 1529]$ $...$
53 $[53, 53, -194w + 1723]$ $...$
59 $[59, 59, -110w - 867]$ $...$
59 $[59, 59, 110w - 977]$ $...$
79 $[79, 79, 650w - 5773]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w + 8]$ $1$
$7$ $[7, 7, -8w + 71]$ $1$